Concepts80
Category
Bridge Tree
A bridge tree is built by contracting every 2-edge-connected component of an undirected graph into a single node, leaving only bridges as edges between nodes.
Tree Distances and Diameter
Tree diameter is the longest simple path in a tree and can be found with two BFS/DFS runs.
Tarjan's SCC Algorithm
Tarjan’s algorithm finds all Strongly Connected Components (SCCs) of a directed graph in a single depth-first search using a stack.
Bridges and Articulation Points
A bridge is an edge whose removal increases the number of connected components; an articulation point is a vertex with the same property.
SPFA (Shortest Path Faster Algorithm)
SPFA is a queue-based optimization of Bellman–Ford that only relaxes edges from vertices whose distance just improved.
Lowest Common Ancestor (LCA)
The Lowest Common Ancestor (LCA) of two nodes in a rooted tree is the deepest node that is an ancestor of both.
MST Properties and Applications
An MST minimizes total edge weight over all spanning trees and has powerful properties such as the cut and cycle properties that guide correct, greedy construction.
Minimum Spanning Tree - Prim
Prim's algorithm builds a Minimum Spanning Tree (MST) by growing a tree from an arbitrary start vertex, always adding the lightest edge that connects the tree to a new vertex.
Minimum Spanning Tree - Kruskal
Kruskal’s algorithm builds a minimum spanning tree (MST) by sorting all edges by weight and greedily picking the next lightest edge that does not form a cycle.
Floyd-Warshall Algorithm
Floyd–Warshall computes the shortest distances between all pairs of vertices in O(n^3) time using dynamic programming.
Dijkstra's Algorithm
Dijkstra's algorithm finds shortest path distances from one source to all vertices when all edge weights are non-negative.
Bellman-Ford Algorithm
Bellman–Ford finds single-source shortest paths even when some edge weights are negative.